suppose point p(4,-9) is translated accoring to the rule (x,y). (X+3,Y-2) what are the coordinates of p? explain

Step-by-step explanation:

"Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imaginary roots.)"

Given one of the roots, we can use either long division or grouping to factor each cubic equation into a binomial and a quadratic.  I'll use grouping.

Then, we can either factor or use the quadratic equation to find the remaining two roots.

1. x³ − 7x + 6 = 0; 1

x³ − x − 6x + 6 = 0

x (x² − 1) − 6 (x − 1) = 0

x (x + 1) (x − 1) − 6 (x − 1) = 0

(x² + x − 6) (x − 1) = 0

(x + 3) (x − 2) (x − 1) = 0

The remaining two roots are both real: -3 and +2.

2. x³ − 3x² + 25x + 29 = 0; -1

x³ − 3x² + 25x + 29 = 0

x³ − 3x² − 4x + 29x + 29 = 0

x (x² − 3x − 4) + 29 (x + 1) = 0

x (x − 4) (x + 1) + 29 (x + 1) = 0

(x² − 4x + 29) (x + 1) = 0

x = [ 4 ± √(16 − 4(1)(29)) ] / 2

x = (4 ± 10i) / 2

x = 2 ± 5i

The remaining two roots are both imaginary: 2 − 5i and 2 + 5i.

3. x³ − 4x² − 3x + 18 = 0; 3

x³ − 4x² − 3x + 18 = 0

x³ − 4x² + 3x − 6x + 18 = 0

x (x² − 4x + 3) − 6 (x − 3) = 0

x (x − 1)(x − 3) − 6 (x − 3) = 0

(x² − x − 6) (x − 3) = 0

(x − 3) (x + 2) (x − 3) = 0

The remaining two roots are both real: -2 and +3.

"Find all the zeros of the function"

For quadratics, we can factor using either AC method or quadratic formula.  For cubics, we can use the rational root test to check for possible rational roots.

4. f(x) = x² + 4x − 12

0 = (x + 6) (x − 2)

x = -6 or +2

5. f(x) = x³ − 3x² + x + 5

Possible rational roots: ±1/1, ±5/1

f(-1) = 0

-1 is a root, so use grouping to factor.

f(x) = x³ − 3x² − 4x + 5x + 5

f(x) = x (x² − 3x − 4) + 5 (x + 1)

f(x) = x (x − 4) (x + 1) + 5 (x + 1)

f(x) = (x² − 4x + 5) (x + 1)

x = [ 4 ± √(16 − 4(1)(5)) ] / 2

x = (4 ± 2i) / 2

x = 2 ± i

The three roots are x = -1, x = 2 − i, x = 2 + i.

6. f(x) = x³ − 4x² − 7x + 10

Possible rational roots: ±1/1, ±2/1, ±5/1, ±10/1

f(-2) = 0, f(1) = 0, f(5) = 0

The three roots are x = -2, x = 1, and x = 5.

"Write the simplest polynomial function with integral coefficients that has the given zeros."

A polynomial with roots a, b, c, is f(x) = (x − a) (x − b) (x − c).  Remember that imaginary roots come in conjugate pairs.

7. -5, -1, 3, 7

f(x) = (x + 5) (x + 1) (x − 3) (x − 7)

f(x) = (x² + 6x + 5) (x² − 10x + 21)

f(x) = x² (x² − 10x + 21) + 6x (x² − 10x + 21) + 5 (x² − 10x + 21)

f(x) = x⁴ − 10x³ + 21x² + 6x³ − 60x² + 126x + 5x² − 50x + 105

f(x) = x⁴ − 4x³ − 34x² + 76x − 50x + 105

8. 4, 2+3i

If 2 + 3i is a root, then 2 − 3i is also a root.

f(x) = (x − 4) (x − (2+3i)) (x − (2−3i))

f(x) = (x − 4) (x² − (2+3i) x − (2−3i) x + (2+3i)(2−3i))

f(x) = (x − 4) (x² − (2+3i+2−3i) x + (4+9))

f(x) = (x − 4) (x² − 4x + 13)

f(x) = x (x² − 4x + 13) − 4 (x² − 4x + 13)

f(x) = x³ − 4x² + 13x − 4x² + 16x − 52

f(x) = x³ − 8x² + 29x − 52

Answer:

[tex]\frac{7}{2}[/tex]in

Step-by-step explanation:

First you must set up an equation. [tex]\frac{1}{2}x=\frac{7}{4}[/tex]

Then, you must solve for x.          [tex]x=\frac{7}{2}[/tex]

Answer:

Fraction of work shift represented by 6 hours = 0.6

Step-by-step explanation:

Total work shift of employee = 10 hours

Time considered  to find fraction = 6 hours

Fraction of work shift represented by 6 hours  6/10=3/5=0.6=60%

Fraction of work shift represented by 6 hours = 0.6

Answer:

0.75

Step-by-step explanation:

Total work shift of an employee is 8 hours

Time consist to find fraction is 6 hours

The fraction of work shift by 6 hours :

[tex]\frac{6}{8}[/tex]  =  [tex]\frac{3}{4}[/tex] = 0.75 = 75%

Answer:

it's rational ..........

Answer:

2/5 is greater

Step-by-step explanation:

to compare you need to make them common denominator, and that could be10. to make both denominators equal to ten just multiply the top and bottom of 2/5 by 2. this will turn it into 4/10. 4/10 is greater than 3/10

The solution is : 2/5> 3/10

2/5 is greater than 3/10

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

Here, we have,

the given fractions are,

2/5 and 3/10

now, we have,

to compare you need to make them common denominator,

and that could be10.

to make both denominators equal to ten just multiply the top and bottom of 2/5 by 2.

i.e. 2*2/5*2

=4/10

this will turn it into 4/10.

now, we get,

4/10 is greater than 3/10

Hence, 2/5> 3/10 , 2/5 is greater than 3/10.

To learn more on fraction click:

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Answer:

36 fliers

Step-by-step explanation:

1/3*72 = 24 fliers posted last week (.333*72)

72-24 = 48 fliers left

1/4*48 = 12 fliers posted this week (.25*48)

48-12= 36 fliers not posted  

Linda has 36 fliers left to post.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given: Linda had 72 fliers to post around town. Last week, she posted 1/3

of them. This week, she posted 1/4 of the remaining fliers.  

1st-week Linda posted 72/3=24 and remaining fliers72-24=48

2nd the week Linda posted 48/4=12 and remaining fliers 48-12=36

∴The remaining fliers left to be posted are 36

Hence, Linda has 36 fliers left to post.

Learn more about the unitary method here:

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*see the given given in the attachment below

Answer:

x = 109°

Step-by-step Explanation:

Since AB is parallel to CF, m<BAE = m<AED = 38° (alternate interior angles are congruent)

Since AE = DE, ∆AED is an isosceles ∆.

The two base angles of any given isosceles ∆ are said to be congruent.

This means, m<EAD = m<EDA = ½(180 - m<AED)

m<EDA = [tex] \frac{1}{2}*(180 - 38) [/tex]

m<EDA = [tex] \frac{1}{2}*(142) = 71 [/tex]

x + m<EDA = 180° (angle on a straight line)

[tex] x + 71 = 180 [/tex]

[tex] x + 71 - 71 = 180 - 71 [/tex]

[tex] x = 109 [/tex]

Value of x = 109°

Answer:Answer:

81 miles

Step-by-step explanation:

From the question 7/10 of the trip has been said to be downhill. It therefore means that 3/10 is not downhill.

Miles = 270

Downhill = 7/10

Not downhill = 3/10

Now we have To calculate Miles that are not downhill (uphill)

But first I calculated for the number of downhill miles

270x7/10

Downhill = 189 miles

To get the number of not downhill miles

I subtracted 189 from the total number of miles on the question.

270 - 189

= 81 Miles.

Therefore 81 Miles of the trip are not downhill.

If you have anymore questions or need clarity please let me know on the comment section. Thank you and Good luck!

Step-by-step explanation:

Answer:

Hey there!

The big square has an area of 6x6 or 36 units.

However, we subtract 8 to get 28 because the 8 white squares do not count.

Let me know if this helps :)

Answer:

28units²

Step-by-step explanation:

6² = 36

36 - 8 = 28

Answer:

A reduce the fraction is

5\1

Answer:

C. 4i-2

Step-by-step explanation:

EDGE 2020

Answer: 0.68

Step-by-step explanation:

given data:

ABC market share = 30%

number of customers surveyed = 800

probability that more than 32% prefers ABC

Solution:

32% of 800

= 256 persons

p ( x ≥ 256 )

= 1 - ( 256/800 )

= 1 - 0.32

= 0.68

the probabiliy that more than 32% of those who carried out the survey would prefer ABC brand is 0.68.

Answer:

344.1 Ib/ft²

Step-by-step explanation:

This has to do with conversion

23.0Ib/gal × 2ft

Step 1

First we convert 23.0lb/gal to Ib/ft³

1 Ib/gal = 7.48051948 Ib/ft³

23.0lb/gal = X Ib/ft³

Cross Multiply

1 Ib/gal × X Ib/ft³ = 23.0lb/gal × 7.48051948 Ib/ft³

X Ib/ft³ = 23.0lb/gal × 7.48051948 Ib/ft³/1 Ib/gal

X Ib/ft³ = 172.05194804 Ib/ft³ =

Step 2

Since 23.0lb/gal = 172.05194804 Ib/ft³

172.05194804 Ib/ft³ × 2 ft

= 344.10389608Ib/ft²

Approximately to 1 significant figure

= 344.1 Ib/ft²

1. Potential Energy = mgh

h = U_g / (mg) = 14 / (17 * 9.81) = 0.084 m above the ground.

2. Kinetic Energy = 1/2 mv^2

m = 2K_e / (v^2) = 2.45 kg

3. U_g = mgh = (1200)(9.81)(24) = 282528 J

4. U_g = mgh = (478)(9.81)(150) = 703377 J

5. U_g = mgh = (100)(9.81)(12.5) = 12262.5 J

6. h = U_g / (mg) = 14 / (17 * 9.81) = 0.084 m above the ground.

7. m = U_g / (gh) = 1500 /  (9.81 * 35) = 4.37 kg

Answer:    2a - 10

Step-by-step explanation:

a represents the number of students in the art club.

The number of students in a school's math club is ten less than twice the number of students in the art club.

ten less = - 10

twice the number of students in the art club = 2*a

2a - 10 = the number of students in the math club

Answer:

(11-1-1)(1+1)

Step-by-step explanation:

revised

Answer: About 88 inches

=============================================

Explanation:

Find the circumference

C = pi*diameter

C = (22/7)*28

C = 88

The tire's circumference is approximately 88 inches. This is the perimeter or distance around the circle. As the bike moves forward one full rotation of the wheel, all of the wheel will touch the ground at some point. The bike will move about 88 inches forward when the wheel does one full rotation.

A good way to visualize this is to imagine cutting the tire so that you can unroll it to lay it out completely flat forming a straight line. This line will be roughly 88 inches long.

Answer:

The solution of the inequation [tex]6\cdot x^{2} \geq 10 + 11\cdot x[/tex] is [tex]\left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right)[/tex].

Step-by-step explanation:

First of all, let simplify and factorize the resulting polynomial:

[tex]6\cdot x^{2} \geq 10 + 11\cdot x[/tex]

[tex]6\cdot x^{2}-11\cdot x -10 \geq 0[/tex]

[tex]6\cdot \left(x^{2}-\frac{11}{6}\cdot x -\frac{10}{6} \right)\geq 0[/tex]

Roots are found by Quadratic Formula:

[tex]r_{1,2} = \frac{\left[-\left(-\frac{11}{6}\right)\pm \sqrt{\left(-\frac{11}{6} \right)^{2}-4\cdot (1)\cdot \left(-\frac{10}{6} \right)} \right]}{2\cdot (1)}[/tex]

[tex]r_{1} = \frac{5}{2}[/tex] and [tex]r_{2} = -\frac{2}{3}[/tex]

Then, the factorized form of the inequation is:

[tex]6\cdot \left(x-\frac{5}{2}\right)\cdot \left(x+\frac{2}{3} \right)\geq 0[/tex]

By Real Algebra, there are two condition that fulfill the inequation:

a) [tex]x-\frac{5}{2} \geq 0 \,\wedge\,x+\frac{2}{3}\geq 0[/tex]

[tex]x \geq \frac{5}{2}\,\wedge\,x \geq-\frac{2}{3}[/tex]

[tex]x \geq \frac{5}{2}[/tex]

b) [tex]x-\frac{5}{2} \leq 0 \,\wedge\,x+\frac{2}{3}\leq 0[/tex]

[tex]x \leq \frac{5}{2}\,\wedge\,x\leq-\frac{2}{3}[/tex]

[tex]x\leq -\frac{2}{3}[/tex]

The solution of the inequation [tex]6\cdot x^{2} \geq 10 + 11\cdot x[/tex] is [tex]\left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right)[/tex].

Answer:

I got (G^B) +F-K+L= (G^B)

Step-by-step explanation:

Answer:

14.48 ft

Step-by-step explanation:

The relation between the location of the focus (c), the vertex on the major axis (a) and the vertex on the minor axis (b) with respect the center is:

b² = a² - c²

From the question:

c = 4 ft

a= 30/2 = 15 ft

Replacing into the equation:

b² = 15² - 4²

b = √209

b = 14.48 ft

So, he should build the whisper chamber at 14.48 ft out from the center along the minor axis

Answer: The answer to this questiojn is 14.48 feet, but if rounded to the nearest tenth, then it should be 14.5 (As it was on my question)

Answer:

Approximately 201 squared inches.

Step-by-step explanation:

So, the composite figure is made up of a square and a semi-circle. The square has side lengths of 12 and the semi-circle has a radius of 6.

The total area of the figure would be the area of the square plus the area of the semi-circle. Thus, find the area of each individual figure.

Square:

The area of a square is given by:

[tex]A=l^2[/tex]

Where l is the side length.

Substitute 12 for l:

[tex]A=(12)^2\\A=144\text{ in}^2[/tex]

So the square is 144 square inches.

Semi-circle:

The area of a semi-circle is given by:

[tex]A=\frac{1}{2}\pi r^2[/tex]

Substitute 6 for r and 3.14 for π:

[tex]A=\frac{1}{2}(3.14)(6)^2\\ A=56.52[/tex]

Therefore, the total area is:

[tex]TA=144+56.52\\TA=200.52\text{ in}^2\approx201\text{ in}^2[/tex]

Answer:

it will be one out six to roll a four

Step-by-step explanation:

there is one being rolled to be a 4 out of six

Answer:

x² - 2

Step-by-step explanation:

To obtain (g ￮ f)(x), substitute x = f(x) into g(x), that is

g(x² - 3)

= x² - 3 + 1

= x² - 2

Answer:

✔ x² - 2

Step-by-step explanation:

EDG 2020

Answer:

I am not totally sure but the answer might be 0.0655.

Answer:

10.67% increase

Step-by-step explanation:

We can find percent increase with (difference/original) x 100

7.47 - 6.75

= 0.72 (difference)

(0.72/6.75) x 100

= 10.67% increase

Answer:

Step-by-step explanation:

19 - 3i - 5 + 4i

14 + i

Answer:

answer is -3

Step-by-step explanation:

-6x+4+3x+3=34

-3x+7=34

-3x=34-7

-3x=27

x=27/-3

x=-3

Answer:

[tex]x=\frac{55}{3},\:y=\frac{22}{3}[/tex]

Step-by-step explanation:

Solve by Substitution ;

[tex]\begin{bmatrix}x+2y=33\\ x-y=11\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:x+2y=33:\quad x=33-2y\\\\\mathrm{Subsititute\:}x=33-2y\\\\\begin{bmatrix}33-2y-y=11\end{bmatrix}\\\\Simplify\\\begin{bmatrix}33-3y=11\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:33-3y=11:\quad y=\frac{22}{3}\\\mathrm{For\:}x=33-2y\\\\\mathrm{Subsititute\:}y=\frac{22}{3}\\x=33-2\times\frac{22}{3}\\\\x=\frac{55}{3}\\\\x=\frac{55}{3},\:y=\frac{22}{3}[/tex]

Answer:

10 m

Step-by-step explanation:

15m - 5m = 10 m

both numbers have m which are alike

Answer: 10m

Step-by-step explanation: you subtract five from fifteen